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DiscretizePDE::femdpop
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    NDSolve`FEM`

    DiscretizePDE::femdpop

    Details

    • This message is generated in the case that the finite element discretization failed.
    • In case a solution is returned by the solver, it is not to be trusted, as some part of the equations failed to be discretized.
    • The various forms of the message indicate in which component the failure occurred.

    Examples

    Basic Examples  (3)

    In the following case, there is a transition from the real to the complex plane:

    Wolfram Language code: NDSolveValue[{D[u[x], {x, 2}] == u[x] ^ (3 / 2) / Sqrt[x], u[0] == 1, u[10] == 0}, u, {x, 0, 10}, Method -> "FiniteElement"]

    One possible workaround is to add a 0 complex component to the equation, such that the solver works in the complex plane:

    Wolfram Language code: NDSolveValue[{D[u[x],{x,2}]==u[x]^(3/2)/Sqrt[x]+0.I,u[0]==1,u[10]==0},u,{x,0,10},Method->"FiniteElement"]

    An alternative in this case is to specify a complex-valued InitialSeeding:

    Wolfram Language code: sol = NDSolveValue[{D[u[x], {x, 2}] == u[x] ^ (3 / 2) / Sqrt[x], u[0] == 1, u[10] == 0}, u, {x, 0, 10}, Method -> "FiniteElement", InitialSeeding -> u[x] == 0.I]

    Visualize the solution making use of Re:

    Wolfram Language code: Plot[Re[sol[x]], {x, 0, 10}, PlotRange -> All]

    Note there is a small complex part of the solution:

    Wolfram Language code: Plot[Im[sol[x]], {x, 0, 10}, PlotRange -> All]

    This message can indicate that an overflow did occur:

    Wolfram Language code: f[x_ ? NumericQ] := If[x <= 1 / 2, 0, 2 * $MaxNumber] NDSolve[{DiffusionPDETerm[{u[x], {x}}, 1] == f[x], DirichletCondition[u[x] == 0, x == 0]}, u, {x, 0, 1}]

    This message can indicate numbers with a different precision than MachinePrecision numbers were generated:

    Wolfram Language code: f[x_ ? NumericQ] := If[x <= 1 / 2, 0, 2 * $MaxMachineNumber] NDSolve[{DiffusionPDETerm[{u[x], {x}}, 1] == f[x], DirichletCondition[u[x] == 0, x == 0]}, u, {x, 0, 1}]